Quasicontinuum Models of Dynamic Phase Transitions

Lev Truskinovsky (1) , Anna Vainchtein (2)

1 LMS - Laboratoire de mécanique des solides
2 Department of Mathematics

We propose a series of quasicontinuum approximations for the simplest lattice model of a fully dynamic martensitic phase transition in one dimension. The approximations are dispersive and include various non-classical corrections to both kinetic and potential energies. We show that the well-posed quasicontinuum theory can be constructed in such a way that the associated closed-form kinetic relation is in an excellent agreement with the predictions of the discrete theory.

Mots clés: kinetic relations; lattice models; nonlocal interactions; gradient models; microkinetics; configurational forces; martensitic phase transitions; Quasicontinuum approximations

Domaines: Mécanique [physics.med-ph]

Lev Truskinovsky, Anna Vainchtein. Quasicontinuum Models of Dynamic Phase Transitions. Continuum Mechanics and Thermodynamics, 2006, 18 (1-2), pp.1-21. ⟨10.1007/s00161-006-0018-5⟩. ⟨hal-00111476⟩